Найти число решений уравнения на данном отрезке+решение.
[tex]2 cos^{2} x-5sinx=4, x-\ \textgreater \ [ -3 \pi ;2 \pi ]. [/tex]
[tex]2 cos^{2} x-5sinx=4, x-\ \textgreater \ [ -3 \pi ;2 \pi ]. [/tex]
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2-2sin²x-5sinx-4=0sinx=a
2a²+5a+2=0
D=25-16=9
a1=(-5-3)/4=-2⇒sinx=-2<-1 нет решения
a2=(-5+3)/4=-1/2⇒sinx=-1/2
x1=-π/6+2πn,n∈z
-3π≤-π/6+2πn≤-2π
-18≤-1+12n≤-12
-17≤12n≤-11
-17/12≤n≤-11/12
n=-1⇒x=-π/6-2π=-13π/6
x2=7π/6+2πk,k∈z
-3π≤7π/6+2πk≤-2π
-18≤7+12k≤-12
-25≤12k≤-19
-25/12≤k≤-19/12
k=-2⇒x=7π/6-4π=-17π/4
k=-1⇒x=7π/6-2π=-5π/6